For the introduction of exponents or for lower-level students, building blocks are particularly suitable for exponent teaching. You simply distribute blocks to the students and have them design tangible models of exponents. For example, to teach squares (x^2), students should design geometrical squares that have the dimensions x by x. Similarly, you can teach x^3 exponents by having students design x by x by x cubes. This activity will help students integrate the practicality of exponents into their own lives.
Scientific notation relies on the knowledge of exponents. You can give students team research projects that require them to find important numbers written in scientific notation. Students will have to work together to come up with ideas as to where to look for such numbers, and may have to pool their resources or conduct online and library research to find these numbers. For additional interaction, tell students they must create poster boards that display these numbers and interpret them during a class presentation.
Paper folding is another hands-on activity that emphasizes the tangibility of exponents, but this particular activity is especially suited for teaching that exponents also apply to fractions. Have students work in groups to fold large sheets of paper. The students should continually fold their pieces of paper in half. The goal of such an activity is for students to see the pattern in the size of the paper as it is folded. Students should find that the size of the paper is predicted by the number of folds according to the exponential P*(1/2)^x, where “P” is the original size of the paper. You may wish to supply students with measuring tools to observe this.
One important area of the application of exponents is probability. You can show students how to predict the end result of certain events or phenomena by letting they play repeating probability games. For example, students can pour a bag of candy in a drawn Yin-Yang symbol from a height of a few inches. By applying the rule to take the candy that does not lie in the Yin part of the symbol away and the rest back into the bag while continuing the process, students will realize that their bags of candy are getting smaller. The rule here is that the candy is diminishing by the exponent of the probability of the candy falling in the Yang section: (1/2)^x. Students should work together to find the mathematical model that can predict how much candy will be left after x times. You can also vary the shape students use to change the probability involved.